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            MERIS Level 1 Radiometric Processor - Equalization Algorithm Specification
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<h3>Algorithm Specification</h3>

<p>The MERIS swath is imaged by a CCD. The radiance at each pixel of a MERIS L1b products results from the measurements
    of 5 cameras spread across the swath, each one imaging a part of the swath with 740 so-called detectors in FR
    (corresponding to 185 mean detectors in RR). This results into 3700 detectors imaging the swath of MERIS FRS product
    (925 in RR). The response of each one of these detectors is calibrated during the routine operation of the
    instrument. Residual uncertainties in the calibration process result into detector-to-detector and camera-to-camera
    systematic radiometric differences. The equalization corrects for these radiometric differences via set of detector
    dependent coefficients correcting for the residual uncertainties in the calibration process. These coefficients are
    retrieved via a methodology described in <a href="#R-1">[R-1]</a> based on observations of the Antarctica plateau
    spread out throughout the MERIS mission lifetime.</p>


<h4>The equalization coefficients and the equalization</h4>

<p>The correction relies on equalization coefficients which are band dependent, detector index dependent and time
    dependent:</p>

<p>c_eq[band, detector, date]<br>
    with detector=[0..nb_detectors-1] ; nb_detector is respectively 924 an 3699 for RR and FR
    and date = julian_day(month, day, year)-julian_day(4,1,2002)
    julian_day(month, day, year) is the Julian day of the day, month and year of the MERIS L1b acquisition.<br>
</p>

<p>The time dependency of these c_eq is actually modelled via a 2nd order polynomial:</p>

<pre>   c_eq[band, detector, date] = c_eq_0[band, detector] +
                                     c_eq_1[band, detector] x date +
                                     c_eq_2[band, detector] x date x date</pre>

<p>For each MERIS L1b spectral band and each reprocessing version there is a corresponding LUT, in ASCII format,
    containing the polynomial coefficients enabling the computation of the equalization coefficient for a given date and
    a given detector index.
    The lines in the LUT corresponds to increasing detector index [0..nb_detectors-1]. On each line one can find c_eq_0,
    c_eq_1 and c_eq_2
</p>

<p>The equalization of a smile corrected L1b RR/FR reflectance product proceeds as follow:</p>
<pre>
    loop over band = 1 to 15
       loop over x= 0 to max_x
          loop over y = 0 to max_y
             detector=detector_index[x, y]
             date = julian_day(month, day, year)-julian_day(4,1,2002)
             c_eq [x, y]=c_eq_0[band, detector] + c_eq_1[band, detector] x date + c_eq_2[band, detector] x date x date
             rho_TOA_equalized[band, x, y] = rho_TOA_smile_corrected[band, x, y] / c_eq [x, y]
          end loop over y
       end loop over x
    end loop over band
</pre>

<p>where the detector_index is the MERIS L1b band of the same name.

    Further details on the retrieval of the equalization coefficients and their application to L1b products can be found
    in <a href="#R-1">[R-1]</a>.
</p>
<br>

<p>
    <b>N.B.1: Equalization of band 11</b><br>
    As explained in [R-1], the equalization coefficient retrieval is not valid for the band 11. All equalisation
    coefficients for band 11 have thus been forced to a values of 1 (no modification of the original L1b product for
    this band)
</p>

<p>
    <b>N.B.2: Correction of the FR data is still only temporary</b><br>
    The FR equalization coefficients for products of the 3rd reprocessing are currently simply obtained by
    linear interpolation of the RR equalisation coefficients.<br>
    This results in an equalization of the FR product only at a max RR spatial frequency and consequently, not all the
    FR detector-to-detector systematic variations are corrected for. A future version of the FR equalisation
    coefficient LUT (3rd reprocessing) will be generated that allow equalization at maximum FR spatial frequency</p>


<h3>Referenced Documents</h3>
<a name="R-1"><b>[R-1]</b></a>:&nbsp;<a
        href="http://org.esa.beam.s3.amazonaws.com/docs/beam/beam-meris-equalization/Bouvet_TN_MERIS_equalization_2nd_reprocessing_v1.3.pdf">
    Bouvet M., Ramoino F. (2010): Equalization of MERIS L1b products from the 2nd reprocessing, ESA TN
    TEC-EEP/2009.521/MB (size: 18.2 MB)</a>
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